Bausch & Lomb Inc. is nearing a deal to sell itself to drug maker Valeant Pharmaceuticals International Inc. for about $9 billion, according to people familiar with the matter—a surprise move that highlights a resurgence in private-equity deal making after years spent in the doldrums.

Bausch & Lomb, which is owned by private-equity firms led by Warburg Pincus LLC, could strike a deal to be sold to Valeant next week, the people said. The deal isn't done yet and could still fall apart, one of the people cautioned....